research papers

Acta Cryst. (2016). B72, 855–863 http://dx.doi.org/10.1107/S2052520616013494 855

Received 6 July 2016

Accepted 22 August 2016

Edited by F. P. A. Fabbiani, University of

Gottingen, Germany

‡ Current affiliation: Center for High Pressure

Science & Technology Advanced Research,

Pudong, Shanghai, People’s Republic of China

Keywords: ferroelectric; neutron diffraction;

phase transitions.

CCDC references: 1500587; 1500588;

1500589; 1500590; 1500591; 1500592;

1500593

Supporting information: this article has

supporting information at journals.iucr.org/b

Neutron and high-pressure X-ray diffraction studyof hydrogen-bonded ferroelectric rubidiumhydrogen sulfate

Jack Binns,a,b*‡ Garry J McIntyrea and Simon Parsonsb

aAustralian Nuclear Science and Technology Organisation, New Illawarra Road, Lucas Heights, NSW 2234, Australia,

and bEaStCHEM School of Chemistry and Centre for Science at Extreme Conditions, The University of Edinburgh, The

King’s Buildings, West Mains Road, Edinburgh EH9 3FJ, Scotland. *Correspondence e-mail: jack.binns@hpstar.ac.cn

The pressure- and temperature-dependent phase transitions in the ferroelectric

material rubidium hydrogen sulfate (RbHSO4) are investigated by a combina-

tion of neutron Laue diffraction and high-pressure X-ray diffraction. The

observation of disordered O-atom positions in the hydrogen sulfate anions is in

agreement with previous spectroscopic measurements in the literature. Contrary

to the mechanism observed in other hydrogen-bonded ferroelectric materials,

H-atom positions are well defined and ordered in the paraelectric phase. Under

applied pressure RbHSO4 undergoes a ferroelectric transition before trans-

forming to a third, high-pressure phase. The symmetry of this phase is revised to

the centrosymmetric space group P21/c, resulting in the suppression of

ferroelectricity at high pressure.

1. Introduction

Rubidium hydrogen sulfate (RbHSO4) is one member of the

family of solid-acid proton conductors, with the general

formula MHAO4, where M = Na+, K+, Rb+, Cs+ or NH4+ and A

= S or Se. These materials have attracted attention as model

hydrogen-bonded ferroelectric materials and for the super-

protonic conduction phases achievable under relatively mild

thermodynamic conditions.

Ferroelectric behaviour in RbHSO4 was first reported by

Pepinsky & Vedam (1960). Their efforts to understand

ferroelectricity in ammonium hydrogen sulfate (NH4HSO4)

focused on ordering within the N—H� � �O hydrogen bonds. To

their surprise, isomorphous RbHSO4 also showed a low-

temperature ferroelectric phase without the requirement of

cation–anion hydrogen bonds. Further measurements have

shown ferroelectric transitions to be prevalent throughout the

MHAO4 family (Sinitsyn, 2010). Subsequent dielectric studies

have revised the transition temperature, and recent piezo-

response-force microscopy settled on the generally accepted

Curie temperature of 264 K (Lilienblum et al., 2013).

Initial structural investigations of MHAO4 in general

focused on low temperatures, and to some degree high pres-

sures, in order to understand the ferroelectric transitions in

these materials. Following the discovery of superprotonic

conductivity, the high-temperature high-pressure regions of

the PT phase diagrams were explored using electrical

conductivity measurements (Ponyatovskii et al., 1985).

Collating over a range of M and A has allowed a general phase

diagram to be produced (Sinitsyn, 2010). The phase diagram

for RbHSO4 is shown in Fig. 1.

Despite the topological similarity amongst the PT phase

diagrams of members of the MHAO4 family, corresponding

ISSN 2052-5206

# 2016 International Union of Crystallography

phases are not necessarily isostructural. RbHSO4 and

RbHSeO4 share a phase sequence superprotonic ! para-

electric! ferroelectric, which occurs at ambient pressure for

RbHSeO4 and at pressures � 0.28 GPa in RbHSO4, reflecting

the ‘chemical pressure’ induced by substituting Se for S

(Suzuki et al., 1979). However, neither the paraelectric nor the

ferroelectric phases are isostructural; RbHSeO4 has space

group P1 in the ferroelectric phase and I2 in the paraelectric

phase (Waskowska et al., 1980; Brach et al., 1983), while the

space groups of the corresponding phases in RbHSO4 are Pc

(phase II, ferroelectric) and P21/c (phase I, paraelectric),

respectively. In RbHSeO4 the ferroelectric transition is due to

proton ordering over a disordered hydrogen bond in contrast

to the proposed mechanism, described below, in RbHSO4

(Itoh & Moriyoshi, 2003).

The well studied analogue CsHSO4 exhibits two ambient-

pressure phases (CsHSO4-II and CsHSO4-III), both crystallize

in P21/c, and therefore neither is ferroelectric. This material

shows a very strong isotopic dependence with the metastable

phase CsHSO4-III only observed in the undeuterated form

(Chisholm & Haile, 2000).

Pepinsky & Vedam (1960) performed the first structural

characterization of RbHSO4; they determined unit-cell para-

meters of phase I in both metrically pseudo-orthorhombic

B21/a and monoclinic P21/c settings. They deduced that the

ferroelectric transition from phase I to II requires the loss of

the 21 screw symmetry element and determined that the

ferroelectric phase must have symmetry Pc, later confirmed by

systematic absence analysis (Pepinsky & Vedam, 1960).

The structures of phases I and II of RbHSO4 were inves-

tigated using X-ray and neutron diffraction by Ashmore &

Petch (1975). The neutron study revealed that the H-atom

positions are fully ordered in the paraelectric phase, in

contrast to paraelectric phases in analogous hydrogen-bonded

ferroelectric materials. By analogy with the disorder–order

transition observed in NH4HSO4, attempts were made to

refine a disordered sulfate model, but the results were

inconclusive.

Dielectric measurements by Ozaki (1980) suggested that

disorder should play an intrinsic role in the phase transition. In

an attempt to confirm this, Itoh et al. (1995) report a disor-

dered paraelectric structure for phase I, citing the large

anisotropic displacement parameters of the O and H atoms of

one HSO4� group, and the successful refinement of a disor-

dered paraelectric phase of NH4HSO4, in support of the

disordered model.

In a subsequent study, Itoh & Moriyoshi (2003) analysed

the temperature dependence of thermal parameters above

and below the Curie temperature, determining the ferro-

electric structure for the first time. They conclude that one

HSO4� anion shows disorder in two O-atom positions rather

than all four. A Raman spectroscopy study by Toupry et al.

(1981) found the temperature dependence of the O—H

frequency to be consistent with a change in ionic orientation.

To complicate matters, an X-ray diffraction study by Nalini

& Row (2003) has cast doubt on the disordered paraelectric

model. They find no evidence of distortion in the sulfate

geometries or significant residual electron density; they record

notable distortions to the sulfate moieties only after cooling

into the ferroelectric phase II.

While investigating the pressure dependence of the I! II

transition, Gesi & Ozawa (1975) identified a high-pressure

phase which was subsequently investigated by Asahi &

Hasebe (1996) at pressures of 0.96 and 1 GPa; this phase III is

described as monoclinic P21.

Clearly there remains some uncertainty as to the structure

of the paraelectric phase I which modern neutron diffraction

data can help to answer. State-of-the-art thermal–neutron

Laue diffractometers allow the collection of extensive

diffraction data to a similar precision as traditional mono-

chromatic instruments with a gain in data collection rate of

one-to-two orders of magnitude (McIntyre et al., 2006). We

show that this technique enables confirmation of the ordered

proton positions as well as yielding accurate O—H bond

lengths which help to clarify the mechanism of ferroelectricity

in rubidium hydrogen sulfate.

2. Methods

Clear, block-like crystals of rubidium hydrogen sulfate

(RbHSO4) were grown from aqueous solutions of equimolar

quantities of RbSO4 and H2SO4.

X-ray diffraction data were collected on a Bruker SMART

APEX II diffractometer with graphite-monochromated

Mo K� radiation (� = 0.71073 A) equipped with an Oxford

Cryosystems variable-temperature device. High-pressure X-

ray diffraction experiments were carried out using a Merrill–

Bassett diamond–anvil cell with a tungsten gasket and tung-

sten carbide backing plates with an accessible semi angle of

40� (Merrill & Bassett, 1974; Moggach et al., 2008). The sample

crystal and a chip of ruby were loaded with Fluorinert FC70 as

the hydrostatic medium. The phase transition from I to II was

initially found to occur on raising the pressure from 0 to

research papers

856 Jack Binns et al. � Ferroelectric rubidium hydrogen sulfate Acta Cryst. (2016). B72, 855–863

Figure 1Pressure–temperature phase diagram of RbHSO4 following Sinitsyn(2010, and references within). Phases I and II can also be described inP21/c and Pc, respectively, by a different choice of unit-cell axes.

0.5 GPa. A second loading was used to fill in extra pressure

points at 0.2 and 0.4 GPa, defining the transition pressure

more precisely. Both loadings were carried out with crystals of

similar sizes (0.10 � 0.12 � 0.20 and 0.10 � 0.15 � 0.20 mm).

Pressure-dependent ruby fluores-

cence was used as a pressure measure

(Piermarini et al., 1975).

Diffraction data were integrated

using SAINT (Bruker, 2007).

Dynamic masks were applied to

account for cell-body shading in the

high-pressure data sets (Dawson et al.,

2004). Absorption corrections were

carried out in SADABS (Sheldrick,

2008). The program SHADE was used

to identify and discard partially

shaded and diamond reflections

(Parsons, 2004). Structures were

solved by direct methods or charge

flipping using SIR92 or SUPERFLIP

(Altomare et al., 1993; Palatinus &

Chapuis, 2007).

Neutron Laue diffraction data were

collected at 300 and 150 K at ambient

pressure on the KOALA Laue

diffractometer, at ANSTO, using a

crystal of dimensions 1.2 � 1.1 �

0.8 mm. Laue patterns were collected

for 4 h each; a total of 12 patterns

were collected at 300 K, 14 at 150 K.

In both cases the vertical rotation

angle was 15� to account for the low

symmetry of these crystals.

The diffraction patterns were indexed and processed using

the program LaueG (Piltz, 2016). Reflection intensities were

integrated with a modified two-dimensional version of the

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Acta Cryst. (2016). B72, 855–863 Jack Binns et al. � Ferroelectric rubidium hydrogen sulfate 857

Table 1Crystal data and details of the structure determination of RbHSO4 phases I and II by neutron Lauediffraction.

For all structures: HO4S�Rb, Mr = 182.54, Z = 8. Experiments were carried out with neutron radiation, � =0.85–1.7 A using the KOALA Laue diffractometer, ANSTO.

Phase II Phase I

Crystal dataCrystal system, space group Monoclinic, Pn Monoclinic, P21/nTemperature (K) 150 300a, b, c (A)† 14.2651 (5), 4.5853 (2), 14.2789 (5) 14.3602 (19), 4.6156 (6), 14.413 (2)� (�)† 117.999 (2) 118.069 (8)V (A3)† 824.66 (6) 842.9 (2)Crystal size (mm) 1.20 � 1.10 � 0.80 1.20 � 1.10 � 0.80

Data collectionNo. of measured, independent and

observed [I > 2.0�(I)] reflections13 194, 2365, 1909 8517, 1612, 1073

Rint 0.097 0.091(sin �/�)max (A�1) 1.114 1.113

RefinementR[F2 > 2�(F2)], wR(F2), S 0.048, 0.112, 0.96 0.051, 0.096, 0.91No. of reflections 1909 1073No. of parameters 253 146No. of restraints 2 0H-atom treatment All H-atom parameters refined All H-atom parameters refined��max, ��min (fm A�3) 0.64, �0.63 0.40, �0.41

Computer programs: MAATEL/ANSTO KOALA control program, LaueG (Piltz, 2016), Laue4 (Piltz, 2011),argonne_boxes (Wilkinson et al., 1988), SIR92 (Altomare et al., 1993), CRYSTALS (Betteridge et al., 2003). † Valuesderived from X-ray diffraction.

Table 2Bond distances and angles for RbHSO4 phases I and II at 300 and 150 K, respectively.

Phase I (300 K)S1—O1 1.553 (5) S1—O31 1.400 (14) O1—H1 0.984 (4)S1—O30 1.481 (13) S2—O8 1.453 (4) S1—O21 1.505 (16)S2—O7 1.444 (5) S1—O20 1.364 (18) S2—O6 1.440 (4)S1—O4 1.439 (5) S2—O5 1.567 (4) O5—H2 0.990 (4)

O1—S1—O4 108.4 (3) O1—S1—O20 109.0 (9) O1—S1—O30 96.9 (5)O1—S1—O21 105.4 (7) O1—S1—O31 107.8 (7) O4—S1—O20 117.2 (9)O4—S1—O30 108.4 (6) O4—S1—O21 108.5 (7) O4—S1—O31 116.2 (9)O5—S2—O8 104.0 (3) O5—S2—O6 108.1 (2) O5—S2—O7 105.5 (3)O7—S2—O8 112.7 (2) O6—S2—O7 113.4 (3) O6—S2—O8 112.3 (3)S1—O1—H1 111.7 (3) S2—O5—H2 114.1 (2)

Phase II (150 K)S1—O1 1.560 (6) S1—O2 1.451 (6) S1—O3 1.451 (6) S1—O4 1.446 (7)S2—O5 1.566 (6) S2—O6 1.458 (6) S2—O7 1.458 (6) S2—O8 1.438 (8)S3—O9 1.580 (7) S3—O10 1.438 (7) S3—O11 1.441 (6) S3—O12 1.446 (8)S4—O13 1.565 (5) S4—O14 1.447 (6) S4—O15 1.466 (6) S4—O16 1.452 (7)O1—H1 1.011 (6) O5—H2 0.996 (6) O9—H3 0.992 (6) O13—H4 1.004 (6)

O1—S1—O2 105.9 (4) O1—S1—O3 103.8 (4) O1—S1—O4 108.5 (4) O2—S1—O3 113.0 (4)O2—S1—O4 112.6 (4) O3—S1—O4 112.4 (4) O5—S2—O8 106.7 (4) O5—S2—O6 107.6 (3)O5—S2—O7 103.9 (4) O7—S2—O8 113.3 (4) O6—S2—O7 111.5 (4) O6—S2—O8 113.1 (4)O9—S3—O11 102.6 (4) O9—S3—O12 106.8 (4) O9—S3—O10 107.1 (4) O10—S3—O12 113.1 (5)O11—S3—O12 112.8 (5) O10—S3—O11 113.5 (5) O13—S4—O14 108.2 (3) O13—S4—O15 104.7 (4)O13—S4—O16 105.4 (4) O14—S4—O15 112.1 (4) O14—S4—O16 113.4 (4) O15—S4—O16 112.4 (3)S1—O1—H1 113.5 (5) S2—O5—H2 113.8 (4) S3—O9—H3 108.4 (5) S4—O13—H4 114.5 (4)

minimum �(I)/I0 algorithm formulated by Wilkinson et al.

(1988) and Prince et al. (1997). The data were normalized to a

single common incident wavelength using the program

LAUE4 for a wavelength spectrum of 0.85�1.7 A (Piltz,

2011). For phase I, data were integrated to a resolution of d =

0.78 A. A total of 8517 reflections were merged to a common

incident wavelength giving an Rmerge = 0.091 with a comple-

teness of 77.1%. Data for phase II were integrated to a

resolution of d = 0.67 A. A total of 13 194 reflections were

normalized and merged to a common incident wavelength

with Rmerge = 0.097 and a completeness of 74.3%. Laue

diffraction suffers from intrinsic harmonic overlap that limits

completeness values to a theoretical maximum of 83.3%

(Cruickshank et al., 1987, 1991). No absorption correction was

applied due to the small crystal size and nearly spherical

crystal form.

All structure refinements were carried out against |F|2 in

CRYSTALS (Betteridge et al., 2003); initial atomic coordi-

nates were derived from X-ray diffraction data. H atoms were

refined with standard riding-model constraints in the refine-

ments against X-ray data. In the refinements against neutron

data, H-atom positional and anisotropic displacement para-

meters were refined freely. Unit-cell dimensions were taken

from X-ray diffraction results at 150 and 300 K. Crystal and

refinement data are given in Table 1. Selected bond lengths

and angles for the different phases discussed in the following

sections are compared in Table 2. Table 3 gives crystal and

refinement details for refinements of high-pressure single-

crystal X-ray diffraction data. Tables of the final refined

atomic coordinates and displacement parameters are given in

the supporting information.

3. Results and analysis

3.1. Ferroelectric phase II

The structure of rubidium hydrogen sulfate phase II was

determined at 150 K in the non-standard polar space group

Pn, with a = 14.2651 (5), b = 4.5853 (2), c = 14.2789 (5) A, and

� = 117.999 (2)�. In the standard Pc setting, used by Pepinsky

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858 Jack Binns et al. � Ferroelectric rubidium hydrogen sulfate Acta Cryst. (2016). B72, 855–863

Table 3Crystal data and details of the structure determination of RbHSO4 phases I, II and III by high-pressure X-ray diffraction.

Phase I I I II IIIPressure (GPa) 0.15 (10) 0.2 (1) 0.4 (1) 0.5 (1) 1.05 (10)

Crystal dataChemical formula HO4SRb HO4SRb HO4SRb HO4SRb HO4SRbMr 182.54 182.54 182.54 182.54 182.54Crystal system, space

groupMonoclinic, P21/n Monoclinic, P21/n Monoclinic, P21/n Monoclinic, Pn Monoclinic, P21/c

Temperature (K) 300 300 300 300 300a, b, c (A) 14.324 (3), 4.6263 (9),

14.401 (7)14.3405 (7), 4.6150 (2),

14.3723 (12)14.334 (5), 4.6197 (17),

14.361 (9)14.166 (5), 4.5982 (9),

14.326 (4)7.3202 (7), 7.765 (2),

7.3247 (8)� (�) 117.74 (3) 118.054 (4) 118.94 (3) 117.68 (3) 110.938 (7)V (A3) 844.6 (5) 839.42 (9) 832.2 (7) 826.4 (5) 388.85 (12)Z 8 8 8 8 4Radiation type Mo K� (� = 0.71073 A) Mo K� (� = 0.71073 A) Mo K� (� = 0.71073 A) Mo K� (� = 0.71073 A) Mo K� (� = 0.71073 A)� (mm�1) 12.088 12.16 12.27 12.36 13.13Crystal size (mm) 0.10 � 0.12 � 0.20 0.10 � 0.15 � 0.20 0.10 � 0.15 � 0.20 0.10 � 0.12 � 0.20 0.10 � 0.12 � 0.20

Data collectionDiffractometer Bruker Kappa APEX2 Bruker Kappa APEX2 Bruker Kappa APEX2 Bruker Kappa APEX2 Bruker Kappa APEX2Absorption correction Multi-scan SADABS Multi-scan SADABS Multi-scan SADABS Multi-scan SADABS Multi-scan SADABSTmin, Tmax 0.26, 0.30 0.09, 0.30 0.08, 0.29 0.24, 0.29 0.17, 0.27No. of measured, inde-

pendent and observed[I > 2.0�(I)] reflec-tions

3119, 754, 620 4260, 781, 673 4115, 754, 658 4613, 1240, 1149 1844, 295, 254

Rint 0.025 0.046 0.048 0.025 0.030(sin �/�)max (A�1) 0.617 0.595 0.588 0.620 0.602

RefinementR[F2 > 2�(F2)], wR(F2),

S0.023, 0.055, 1.02 0.056, 0.157, 0.99 0.069, 0.139, 1.04 0.044, 0.116, 0.83 0.032, 0.073, 0.98

No. of reflections 620 780 658 1149 254No. of parameters 110 110 110 99 55No. of restraints 0 20 28 2 13H-atom treatment H-atom parameters

constrainedH-atom parameters

constrainedH-atom parameters

constrainedH-atom parameters

constrainedH-atom parameters

constrained��max, ��min (e A�3) 0.35, �0.35 1.03, �0.73 1.27, �0.99 0.84, �1.01 0.50, �0.35Absolute structure – – – (Flack, 1983), 562

Friedel pairs–

Absolute structureparameter

– – – 0.236 (18) –

Computer programs: APEX2 (Bruker, 2007), SADABS (Sheldrick, 2008), SIR92 (Altomare et al., 1993), CRYSTALS (Betteridge et al., 2003).

& Vedam (1960) and Itoh & Moriyoshi (2003), the unit-cell

dimensions are a = 14.265, b = 4.585, c = 14.701 A, and � =

120.955�. The Pn setting was used here on account of its

(slightly) smaller value of � and because it makes the under-

lying pseudo-orthorhombic and pseudo-hexagonal symmetry

more obvious through the near equality of a and c.

The final agreement factor for the refinement against the

neutron diffraction data for phase II was low, R[F2 > 2�(F2)] =

0.048. Possibilities for twinning were investigated by coset

decomposition, however, none of the applied twin laws

improved data fitting.

Neutron diffraction data were refined against structures

derived from ambient-pressure X-ray diffraction and the

refined structures from each radiation are the same within

error, with the exception of H-atom positions and displace-

ment parameters. Geometric parameters quoted in the

following discussion of the ambient-pressure structures are

derived from neutron diffraction data.

The asymmetric unit in phase II consists of four rubidium

cations and four hydrogen sulfate anions. HSO4� anions form

infinite hydrogen-bonded chains in the b direction, running

parallel to ribbons of Rb+ cations (Fig. 2a). These chains have

similar O� � �H distances of 1.551 (6) and 1.580 (7) A, but

different O—H� � �O angles of 174.2 (7) and 172.7 (6)�

reflecting the two orientations adopted by the disordered

anion on cooling. The S—O(—H) bond is elongated by

0.12 (1) A on average relative to the other three S—O bonds

and O—S—O bond angles range from 103.13 (12)� to

113.35 (15)�. The remaining 12 S—O bond lengths range in

length from 1.438 (7) to 1.466 (6) A. Each Rb+ cation is

coordinated by six HSO4� anions, four anions coordinate in a

bidentate fashion, and the remaining two coordinate via a

single O atom giving a total coordination number of ten (Fig.

2b). Rb—O coordination distances vary between 2.881 (4) and

3.443 (6) A with the two shortest Rb—O bonds formed with

the monodentate HSO4� anions. The origin of this structure

was selected to match that of phase I to facilitate comparison.

3.2. Paraelectric phase I

At room temperature rubidium hydrogen sulfate has unit-

cell dimensions a = 14.3602 (19), b = 4.6156 (6), c =

14.413 (2) A, and � = 118.069 (8)�, space group P21/n, the non-

standard setting chosen to give a smaller � angle closer to 90�.

The asymmetric unit of phase I contains two Rb+ cations

and two HSO4� anions. The hydrogen-bonded chains of anions

observed in phase II persist in phase I, and indeed the struc-

tures of both phases are generally rather similar. Each HSO4�

is distorted by the elongation of the S—O(—H) bond by

0.121 (4) A. Beyond the elongation of the S—O(—H) bond,

the remaining S—O bonds are statistically equal, bond angles

within HSO4� units range from 103.60 (15)� to 116.7 (16)�. At

300 K, one rubidium cation (Rb1) is coordinated to six

hydrogen sulfate anions in the same manner as at 150 K, four

HSO4� bonding in a bidentate fashion, the remaining two

being monodentate. The other Rb atom (Rb2) is nine-coor-

dinate at 300 K, with three bidentate HSO4� and three

monodentate HSO4� anions. Rb–O bond distances vary over a

similar range to those in phase II, from 2.924 (3) to

3.256 (4) A. The reduction in coordination number is caused

by the shift in HSO4� orientation through the II–I transition,

which results in a long Rb—O distance of 4.107 (4) A

compared with the bonding distance of 3.443 (6) A in phase II.

In phase I, both hydrogen-bonded chains are statistically

similar, including the two hydrogen bonds formed by the

disordered HS(1)O4� anions. For HS(1)O4

� chains the O� � �H

distance is 1.604 (14) A to O30, and 1.521 (15) A to O31, O—

H� � �O angles are 170.3 (5) and 172.7 (5)�, respectively.

Hydrogen-bonded chains formed by HS(2)O4� anions have

O� � �H distances of 1.610 (4) A with an O—H� � �O angle of

171.2 (3)�.

In light of the disagreement in the literature regarding the

disordered nature of the HS(1)O4� anion, both ordered and

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Acta Cryst. (2016). B72, 855–863 Jack Binns et al. � Ferroelectric rubidium hydrogen sulfate 859

Figure 2(a) Four unique hydrogen-bonded chains of hydrogen sulfate anionsalong the b axis in the asymmetric unit of phase II at 150 K; (b) the ten-atom coordination environment of Rb1, essentially identical to Rb2–4.The shortest Rb—O distances are given in the figure and are formed tothe monodentate hydrogen sulfate anions. Rb: blue, S: yellow, O: red, H:white. Ellipsoids are shown at the 50% probability level.

disordered models were refined against the neutron diffrac-

tion data for phase I, and the corresponding asymmetric units

are shown in Figs. 3(a) and (b).

As Itoh & Moriyoshi (2003) note, anomalously large atomic

displacement parameters (ADPs) are observed for the O

atoms of the HS(1)O4� tetrahedron, in particular O3 which

acts as the donor in the O1—H1� � �O3 hydrogen-bonded

infinite chain (Fig. 3a). This is clearly illustrated by comparison

of the average equivalent isotropic displacement parameter

(Ueq) for O atoms bound only to S [0.0456 (8) A2] and that of

O3 [0.0707 (12) A2].

These results, along with earlier spectroscopic work by

Ozaki (1980) and Toupry et al. (1981), are consistent with

dynamic disorder in the two oxygen positions. Two O atoms of

HS(1)O4� can be refined against the neutron data obtained in

the present study over two split positions each with refined

occupancies of 0.51 (2) and 0.49 (2) for O20/21 and 0.50 (2) for

O30/31. H atoms, located in difference maps, occupy well

defined positions with no indication of split occupancy. The

final agreement factor for the ordered model was R = 0.0552,

that for the disordered model is R = 0.0508. This disordered

model results in Ueq values for O30 and O31 that do not differ

significantly from the average oxygen Ueq values, in contrast to

the ordered model.

Below Tc, interaction between HSO4� ions outweighs

thermal motion (Toupry et al., 1981). The paraelectric to-

ferroelectric transition therefore involves the ordering of two

alternative anionic orientations representing minima between

which HS(1)O4� ions are able to oscillate in the paraelectric

phase. Symmetry analysis using ISODISTORT (Campbell et

al., 2006) indicates that the phase I to II transition occurs via a

ferroelectric mode of �2� symmetry, which is IR active, but

Raman inactive. The absence of any mode softening as

reported by Toupry et al. is in agreement with Raman and IR

selection rules for this symmetry.

Comparison of the phase I and II structures in Figs. 3(c) and

(d) shows the two disordered sites in the HS(1)O4-I unit are

overlapped orientations of the HS(1)O4-II and HS(3)O4-II

units in the ferroelectric phase II. Fig. 3(c) shows two asym-

metric units in phase I related by inversion symmetry. As the

sample is cooled, half the HS(1)O4-I units occupy the orien-

tation of HS(1)O4-II with the other half occupying the

HS(3)O4-II orientation as shown in Fig. 3(d). This breaks the

inversion symmetry creating a non-centrosymmetric polar

structure and giving rise to spontaneous electric polarization.

As is implied by the ferroic nature of this transition, this

transition occurs via a translationengeleiche maximal group–

subgroup relationship between phases I and II. In such a

transition unit-cell dimensions remain essentially fixed and the

point-group symmetry of the crystal is decreased (Muller,

2013).

3.3. High-pressure X-ray diffraction

RbHSO4 is reported to undergo two phase transitions with

pressure at room temperature. Above 0.4 GPa phase I (P21/n)

undergoes a transition, which has been described as second-

order (Kalevitch et al., 1995; Itoh & Moriyoshi, 2003), to phase

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860 Jack Binns et al. � Ferroelectric rubidium hydrogen sulfate Acta Cryst. (2016). B72, 855–863

Figure 3(a) Asymmetric unit of RbHSO4 phase I, ordered model. The enlarged ADPs of O2 and O3 are clearly visible; (b) asymmetric unit of RbHSO4 phase I,disordered model, splitting of O2 and O3 sites results in a lower R-factor and is supported by dielectric and solid-state NMR measurements. The twoorientations of the disordered HS(1)O4-I anions shown in (c) are approximately equivalent to the phase II anions HS(1)O4-II and HS(3)O4-II shown in(d).

II (Pn), which then undergoes a first-order transformation at

0.75 GPa to phase III reported to be P1121 (Asahi & Hasebe,

1996).

In this work single-crystal X-ray diffraction data were

collected at pressures of 0.15 (10), 0.2 (1), 0.4 (1), 0.5 (1) and

1.05 (10) GPa.

Up to 0.4 GPa the unit-cell volume decreases by 10.8 (8) A3

(1.3%), axial compression is small, the most significant change

is in c with a reduction of 0.052 (9) A, a decreases by

0.026 (5) A, and b remains unchanged within error. The �angle increases by 0.871 (3)� (0.73%). Over the I�II phase

transition, the unit-cell volume falls continuously, � decreases

by 1.26 (4)�, accompanied by decreases in a and b of

�0.166 (7) and �0.021 (2) A, respectively, and as a result the

unit-cell volume falls by 5.7 (9) A3 (0.7%; Fig. 4a). Systematic

absences were strongly suggestive of a loss of the 21 screw axis

in phase II, although refinements were attempted in both

P21/n and Pn.

The structure of phase III has previously been described by

Asahi & Hasebe (1996) as non-standard monoclinic, P1121, a =

7.360 (4), b = 7.346 (4), c = 7.756 (2) A, = 110.86 (4)� at

1.00 (3) GPa. The present X-ray diffraction measurements at

1.1 (1) GPa have found phase III to be monoclinic, P21/c, a =

7.3202 (7), b = 7.765 (2), c = 7.3247 (8) A, � = 110.938 (7)�.

The change in hI/�(I)i for reflections of the type k = 2n + 1

with pressure is shown in Fig. 4(b), indicating the presence of

the 21 screw symmetry element in phases I and III. For phase

II, refinement in P21/n resulted in a significantly higher

agreement factor, R = 0.0991 versus R = 0.0437 in Pn,

confirming the systematic absence analysis. The resulting

structure for phase III is similar to that described by Asahi &

Hasebe (1996), although with space-group symmetry reas-

signed (Fig. 5). Of the 279 reflections affected by the presence

of c-glide symmetry, three have I/�(I) > 3, hI/�(I)i = 0.5, hIi =

0.3. This structure is isostructural

with the corrected structure of

CsHSO4-II reported by Chisholm

& Haile (2000).

The diffraction pattern showed

clear signs of pseudo-merohedral

twinning, with two domains

indexed to the above cell related by

a twofold rotation about the ½�1101�

direction, and reflections are

related by the twin law expressed

below, as determined using the

program CELL NOW (Sheldrick,

2005).

0 0 �110 �11 0�11 0 0

0@

1A

The twinning reflects the pseudo-

orthorhombic symmetry of the

lattice (present because a ’ c)

leading to a two-domain twin. The

refined twin scale factor was

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Acta Cryst. (2016). B72, 855–863 Jack Binns et al. � Ferroelectric rubidium hydrogen sulfate 861

Figure 4(a) Change in unit-cell volume for phases I and II with pressure; (b)change in hI/�(I)i for reflections of the type k = 2n + 1, with pressure,showing the clear presence of a 21 screw symmetry element in phases Iand III.

Figure 5(a) Unit cell of RbHSO4 phase III, two alternating HSO4

� hydrogen-bonded chains form along the c axis;(b) coordination environment of Rb in phase III.

0.541 (11). Given the very minor

structural differences between

phases I and II, the following

discussion of the structural changes

is applicable to both I and II.

The rows of cations along the

[101]III direction (equivalent to

[010]I) are preserved through the

transition, with a shift in Rb+ posi-

tions occurring within the acI plane

(equivalent to the [101]-bIII plane).

The Rb+ cations shift by

0.99 (2) A along the [101]I

direction (along bIII) in an alter-

nating fashion, forming corrugated

hexagonal nets parallel to (100)III.

As a result, the asymmetric

diamond-shaped channels in the bI

direction (along which the infinite

HSO4�� � �HSO4

� chains form)

transform to staggered hexagonal

channels to accommodate the

HSO4� reorientations shown in Fig.

6. Accompanying this shift, the

HSO4� anions reorient, breaking

the infinite hydrogen-bonded

chains along bI. The new arrange-

ment consists of two symmetry-

related, zigzagging infinite chains

along the cIII direction, with an

O(H)� � �O distance of 2.576 (15) A.

These new chains form at an angle

of �III/2 = 55.5� to the direction of

the chains in phase I. As a result,

the asymmetric diamond-shaped

channels in the bI direction (along

which the infinite HSO4�� � �HSO4

� chains form) transform to

staggered hexagonal channels to accommodate the HSO4�

reorientations. The alternating chain direction regenerates the

inversion symmetry of phase I, removing the polarization

present in phase II.

There are no statistically significant changes to bond lengths

within the HSO4� anions up to 1.1 GPa. In phase III, rubidium

cations are coordinated by 11 O atoms, an increase in coor-

dination number of one as shown in Fig. 5(b). Two HSO4�

anions bind in a bidentate fashion through two O atoms, the

remaining anions bind in a monodentate manner. Rubidium–

oxygen bonds adopt a wider range of lengths in this phase,

from 2.861 (9) to 3.589 (12) A, and as a result the average

Rb—O bond length [3.121 (9) A] is the same within error as at

ambient pressure [3.077 (3) A]. This is an example of the

widely observed ‘pressure–distance paradox’ whereby pres-

sure-driven coordination number increases are accompanied

by an increase in bond length (Kleber & Wilke, 1969).

The pressure response of donor–acceptor distances are

shown in Fig. 7. Up to 0.4 GPa the hydrogen-bonding

distances in the HS(1)O4,I and HS(2)O4,II chains remain

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862 Jack Binns et al. � Ferroelectric rubidium hydrogen sulfate Acta Cryst. (2016). B72, 855–863

Figure 6Reorientation of Rb+ cations and HSO4

� anions through the pressure-induced phase transition. (a)Illustrates the asymmetric diamond channels in phase I, shifts in Rb+ positions leading to the formation ofstaggered hexagonal channels containing reoriented HSO4

� anions. (b) Formation of a new hydrogen-bonding system in phase III. The linear chains along bI are broken by the movement of HSO4

� anions toform new zigzagging chains along the cIII direction.

Figure 7Changes in hydrogen bonding donor–acceptor distances (D� � �A) withpressure in RbHSO4. The two symmetry-independent hydrogen-bondedchains in phase I are shown by open and closed black squares. Phase IIdata are shown by open red circles. Phase III datum is shown by a closedblue circle.

distinct with the difference in O(H)� � �O distances increasing

from 0.074 (6) A at ambient pressure to 0.13 (2) A at 0.4 GPa.

Upon the transition to phase II, O(H)� � �O distances are not

statistically distinguishable for each symmetry-independent

chain. The increase in symmetry over the phase II ! III

transition means that phase III contains only one unique

hydrogen bond, in which the O(H)� � �O distance is

2.576 (15) A, which is not significantly different to the

ambient-pressure values. Table 3 lists selected crystal structure

determination details for each phase at high pressure.

4. Conclusions

The paraelectric ! ferroelectric transition in RbHSO4 has

been investigated with neutron Laue diffraction. H atoms

were refined to singly occupied positions with no sign of

possible double-well occupancy. One HSO4� moiety could be

refined with two disordered O atoms; this disordered model

resulted in better agreement with the neutron data over an

ordered model with distended oxygen ADPs. Pressure-driven

phase transitions were investigated by a single-crystal X-ray

diffraction isothermal pressure series up to 1.1 (1) GPa. The

first-order reconstructive phase transition from ferroelectric

phase II to phase III was investigated, and the space group

revised from P21 and P21/c.

Acknowledgements

We thank the Bragg Institute, ANSTO, for the allocation of

neutron beamtime under proposal 3588. JB wishes to thank

EPSRC and the Australian Government for funding.

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